Distributed Tree Kernels

In this paper, we propose the distributed tree kernels (DTK) as a novel method to reduce time and space complexity of tree kernels. Using a linear complexity algorithm to compute vectors for trees, we embed feature spaces of tree fragments in low-dimensional spaces where the kernel computation is directly done with dot product. We show that DTKs are faster, correlate with tree kernels, and obtain a statistically similar performance in two natural language processing tasks.Comment: ICML201

Encasement as a morphogenetic mechanism: The case of bending

We study how the encasement of a growing elastic bulk within a possibly differently growing elastic coat may induce mechanical instabilities in the equilibrium shape of the combined body. The inhomogeneities induced in an incompressible bulk during growth are also discussed. These effects are illustrated through a simple example in which a growing elastic cylinder may undergo a shape transition towards a bent configuration.Comment: 17 pages, 3 figure

Parsing with CYK over Distributed Representations

Syntactic parsing is a key task in natural language processing. This task has been dominated by symbolic, grammar-based parsers. Neural networks, with their distributed representations, are challenging these methods. In this article we show that existing symbolic parsing algorithms can cross the border and be entirely formulated over distributed representations. To this end we introduce a version of the traditional Cocke-Younger-Kasami (CYK) algorithm, called D-CYK, which is entirely defined over distributed representations. Our D-CYK uses matrix multiplication on real number matrices of size independent of the length of the input string. These operations are compatible with traditional neural networks. Experiments show that our D-CYK approximates the original CYK algorithm. By showing that CYK can be entirely performed on distributed representations, we open the way to the definition of recurrent layers of CYK-informed neural networks.Comment: The algorithm has been greatly improved. Experiments have been redesigne

Hidden scaling patterns and universality in written communication

The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agent's `proper time' measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bi-modal character, which is empirically borne out by our new years-long data on email. These novel perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, emergency handling.Comment: 27 pages, 10 figure

New activity pattern in human interactive dynamics

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new universal pattern for how the reactive dynamics of individuals is distributed across the set of each agent's contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to each different correspondent of a given writer, generate a family of heavy-tailed distributions, which have largely the same features for all agents, and whose characteristic times grow exponentially with the rank of each correspondent. We furthermore show that this universal behavioral pattern emerges robustly by considering weighted moving averages of the priority-conditioned response-time probabilities generated by a basic prioritization model. Our findings clarify how the range of priorities in the inputs from one's environment underpin and shape the dynamics of agents embedded in a net of reactive relations. These newly revealed activity patterns might be present in other general interactive environments, and constrain future models of communication and interaction networks, affecting their architecture and evolution.Comment: 15 pages, 7 figure

On solutions of one-dimensional stochastic differential equations driven by stable Lévy motion

AbstractWe consider the stochastic differential equation dXt= b(Xt)dZt, t⩾o,where b is a Borel measurable real function and Z is a symmetric α-stable Lévy motion. In Section 1 we study the convergence of certain functionals of Z and in particular, we extend Engelbert and Schmidt 0–1 law (for functionals of the Wiener process) to functionals of a symmetric α-stable Lévy motion with 1 < α ⩽ 2. In Section 2 we study the existence of weak solutions for the above equation. When 0 < α < 1 or 1 < α ⩽ 2 we prove a sufficient existence condition. In the case 1 < α ⩽ 2, we extend Engelbert and Schmidt's necessary and sufficient existence condition (for the equation driven by a Wiener process) to the above equation: we prove that, for every α there exists a nontrivial solution starting from α, if and only if |b| α is locally integrable. In Section 3 we study “local” solutions. We also prove a result relating “local” and “global” solutions

Intermittency in crystal plasticity informed by lattice symmetry

We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts for the infinite and discrete symmetry group G of the underlying periodic lattice. This generates a complex energy landscape with countably-many G-related wells in strain space, whereon the material evolves by energy minimization under the loading through spontaneous slip processes inducing the creation and motion of dislocations without the need of auxiliary hypotheses. Multiple slips may be activated simultaneously, in domains separated by a priori unknown free boundaries. The wells visited by the strain at each position and time, are tracked by the evolution of a G-valued discrete plastic map, whose non-compatible discontinuities identify lattice dislocations. The main effects in the plasticity of crystalline materials at microscopic scales emerge in this framework, including the long-range elastic fields of possibly interacting dislocations, lattice friction, hardening, band-like vs. complex spatial distributions of dislocations. The main results concern the scale-free intermittency of the flow, with power-law exponents for the slip avalanche statistics which are significantly affected by the symmetry and the compatibility properties of the activated fundamental shears.Comment: 13 pages, 4 figure

Strain intermittency in shape-memory alloys

We study experimentally the intermittent progress of the mechanically induced martensitic transformation in a Cu-Al-Be single crystal through a full-field measurement technique: the grid method. We utilize an in- house, specially designed gravity-based device, wherein a system controlled by water pumps applies a perfectly monotonic uniaxial load through very small force increments. The sample exhibits hysteretic superelastic behavior during the forward and reverse cubic-monoclinic transformation, produced by the evolution of the strain field of the phase microstructures. The in-plane linear strain components are measured on the sample surface during the loading cycle, and we characterize the strain intermittency in a number of ways, showing the emergence of power-law behavior for the strain avalanching over almost six decades of magnitude. We also describe the nonstationarity and the asymmetry observed in the forward versus reverse transformation. The present experimental approach, which allows for the monitoring of the reversible martensitic transformation both locally and globally in the crystal, proves useful and enhances our capabilities in the analysis and possible control of transition-related phenomena in shape-memory alloys.Comment: Four supplementary video

Distributed Smoothed Tree Kernel

In this paper we explore the possibility to merge the world of Compositional Distributional Semantic Models (CDSM) with Tree Kernels (TK). In particular, we will introduce a specific tree kernel (smoothed tree kernel, or STK) and then show that is possibile to approximate such kernel with the dot product of two vectors obtained compositionally from the sentences, creating in such a way a new CDSM

Exploiting Transitivity in Probabilistic Models for Ontology Learning

Capturing word meaning is one of the challenges of natural language processing (NLP). Formal models of meaning such as ontologies are knowledge repositories used in a variety of applications. To be effectively used, these ontologies have to be large or, at least, adapted to specific domains. Our main goal is to contribute practically to the research on ontology learning models by covering different aspects of the task. We propose probabilistic models for learning ontologies that expands existing ontologies taking into accounts both corpus-extracted evidences and structure of the generated ontologies. The model exploits structural properties of target relations such as transitivity during learning. We then propose two extensions of our probabilistic models: a model for learning from a generic domain that can be exploited to extract new information in a specific domain and an incremental ontology learning system that put human validations in the learning loop. This latter provides a graphical user interface and a human-computer interaction workflow supporting the incremental leaning loop